Evaluate the integral. \int_{0}^{1}\int_{0}^{\pi}\int_{0}^{\pi}y*\cos(z)dx dy dz

Brennan Flores 2021-10-25 Answered
Evaluate the integral.
010π0πycos(z)dxdydz
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Expert Answer

Demi-Leigh Barrera
Answered 2021-10-26 Author has 97 answers
Step 1
Given that: 010π0πycos(z)dxdydz
Step 2
As the given integral have constant limits.
So, each integral can be evaluated separately.
Thus, 010π0πycos(z)dxdydz=011dx0πydy0πcoszdz
=[x]01[y22]0π[sinz]0π
=[10][π2022][sinπsin0]
=1×π22×0
=0
So, 010π0πycos(z)dxdydz=0
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